Script for rendering a specific frame n-times
The following works for me.
Add a follow path constraint to your camera. It is the offset of this constraint that we will change in order to move the camera. 


camera_name: name of the camera you want to move
constraint_name: name of the constraint whose offset you want to animate
scene_name: name of your scene
output_location: where the rendered frames will be saved; if this is /some/path/tiger then your frames will be stored as /some/path/tiger0, /some/path/tiger1, ... (with file extensions added if this is in your scene settings)
initial_offset, final_offset: initial and final offset that will be used for the constraint
nr_frames: the total number of frames to render


Here's the code. It's very simple. To run it, just copy-paste into a new file in Blender's text editor, adjust settings and click Run Script.

#### Adjust these settings ####
camera_name = "Camera"
constraint_name = "Follow Path"
scene_name = "Scene"
output_location = "c:\\zoo\\elephant"

initial_offset = -10
final_offset = 10
nr_frames = 16
###############################

import bpy

# save now, so that we can restore these later
original_offset = bpy.data.objects[camera_name].constraints[constraint_name].offset
original_filepath = bpy.data.scenes[scene_name].render.filepath

# render the frames
for i in range(0, nr_frames):
    offset = initial_offset + (final_offset - initial_offset) * i / (nr_frames - 1)
    bpy.data.objects[camera_name].constraints[constraint_name].offset = offset
    bpy.data.scenes[scene_name].render.filepath = output_location + str(i)
    bpy.ops.render.render(write_still = True)

#restore original values
bpy.data.scenes[scene_name].render.filepath = original_filepath
bpy.data.objects[camera_name].constraints[constraint_name].offset = original_offset